Iterated discrete polynomially based Galerkin methods

摘要

Golberg and Bowman [Appl. Math. Comput. 96 (1998) 237] have studied polynomially based discrete Galerkin method for Fredholm and Singular integral equations. In this paper we consider polynomially based iterated discrete Galerkin method for solution of operator equations and for eigenvalue problem associated with an integral operator with a smooth kernel. We show that the error in the infinity norm, both for approximation of operator equation and of spectral subspace, is of the order of n−r, where n is the degree of the polynomial approximation and r is the smoothness of the kernel. Thus the iterated discrete Galerkin solution improves upon the discrete Galerkin solution, which was shown to be of order n−r+1 by Golberg and Bowman [Appl. Math. Comput. 96 (1998) 237]. We also give a shorter proof of the result by Golberg and Bowman which states that the error in 2-norm in discrete Galerkin method is of the order of n−r.